Within the framework of the coding of multi-channel audio signals, two approaches are particularly known and used.
The first and older consists in matrixing the channels of the original multi-channel signal so as to reduce the number of signals to be transmitted. By way of example, the Dolby® Pro Logic® II multi-channel audio coding method carries out the matrixing of the six channels of a 5.1 signal into two signals to be transmitted. Several types of decoding can be carried out so as to best reconstruct the six original channels.
The second approach, called parametric audio coding, is based on extracting spatialization parameters so as to reconstitute the listener's spatial perception. This approach is based mainly on a method called “Binaural Cue Coding” (BCC) which is aimed on the one hand at extracting and then coding the indices of the auditory localization and on the other hand at coding a monophonic or stereophonic signal arising from the matrixing of the original multi-channel signal.
Furthermore, an approach exists which is a hybrid of the above two approaches based on a procedure called “Principal Component Analysis” (PCA). Specifically, PCA can be seen as a dynamic matrixing of the channels of the multi-channel signal to be coded. More precisely, PCA is obtained through a rotation of the data whose angle corresponds to the spatial position of the dominant sound sources at least for the stereophonic case. This transformation is moreover considered to be the optimal decorrelation procedure which makes it possible to compact the energy of the components of a multi-component signal. An exemplary PCA-based stereophonic audio coding is disclosed in documents WO 03/085643 and WO 03/085645.
Specifically, FIG. 11 is a schematic view illustrating an encoder 109 for PCA-based stereophonic coding according to the above prior art.
This encoder 109 carries out adaptive filtering of the components arising from the PCA of the original stereo signal comprising the channels L and R.
The encoder comprises rotation means 102, PCA means 104, prediction filtering means 106, subtraction means 108, multiplication means 110, addition means 112, first and second audio coding means 129a and 129b. 
The rotation means 102 carry out a rotation of the channels L and R according to an angle α thus defining a principal component y and a residual component r. The angle α is determined by the PCA means 104 so that the principal component y exhibits a higher energy than that of the residual component r.
The multiplication means 110 multiply the residual component r by a scalar γ. The result of the multiplication rγ is added by the addition means 112 to the principal component y. The result of the addition rγ+y is introduced into the prediction filtering means 106.
The filtering parameter Fp which defines the prediction filtering means 106 is coded by the second coding means 129b to generate a coded filtering parameter Fpe.
Moreover, the result of the addition rγ+y is also coded by the first coding means 129a to generate a coded principal component ye.
Thus, the procedure consists in determining the parameters of the prediction filtering means such that these filtering means can generate an estimation of the residual component r arising from the PCA on the basis of the principal component y which has the greatest energy.
FIG. 12 is a schematic view illustrating a decoder 115 for decoding a stereophonic signal coded by the encoder of FIG. 11.
The decoder 115 comprises first and second decoding means 141a and 141b, filtering means 120, inverse rotation means 118 and addition and multiplication means 122a and 122b. 
The decoder 115 then carries out the inverse operation by decoding the principal component y′e by the first decoding means 141a forming a decoded principal component y′, then by carrying out its filtering by the filtering means 120 into a filtered residual component r′ on the basis of the filtering parameters Fp.
The multiplication means 122b multiply the filtered residual component r′ with the scalar γ forming the product r′γ. The addition means 122a make it possible to subtract r′γ from the decoded principal component y′.
The inverse rotation means 118 apply the inverse rotation matrix as a function of the angle of rotation a to the signals y′ and r′ so as to generate the channels L′ and R′ of the decoded stereophonic signal.
However, the PCA carried out according to the prior art does not adapt to the constraints of the transmission network and does not make it possible to obtain a fine characterization of the signals to be coded.